摘要
題 目: 奈米碳管強度及勁度之估測
研 究 生: 侯彥嘉
指導教授: 胡潛濱
奈米碳管為目前新興的補強材料，它具有優秀的機械性質，如高強度、高韌性、重量輕等特性；本文主要結合有限元素法及分子動力學去估測其機械性質，參考相關文獻提出的方法並做修改。文中使用有限元素軟體ANSYS裡樑元素來模擬連結相鄰兩碳原子之共價鍵，導入modified Morse potential 為共價鍵中的勢能函數，而層間凡德瓦力則模擬成彈簧元素。藉由非線性樑理論推導出樑元素之材料性質，再由軟體模擬碳管並計算整體的機械性質及估測整體強度。從結果得知，不同形態的單壁奈米碳管其楊氏係數約為1-1.2 TPa左右、浦松比約為0.17-0.25左右，而降伏強度則落在20-30 GPa範圍內。參考其他文獻的數值比較，本文結果有一定程度的吻合；顯示研究方法有相當程度的正確性與可靠性。在極限強度方面，因未考慮Stone-Wales defect 等結構變化，故數值結果皆小於相關文獻。
本文也以有限元素法的觀點在機械性質方面做討論，將模擬共價鍵之樑元素做切割並增加元素量來做收斂性分析，文中也討論奈米碳管的長徑比對機械性質的影響，比較兩者的差異性，其結果確定已收斂(<0.5%)。

ABSTRACT
Subject: Estimation of Strength and Stiffness of Carbon Nanotubes
Graduate: Yan-Jia Hou
Advisors: Chyanbin Hwu
Since its discovery, the superior properties of carbon nanotubes (CNTs),such as high strength, toughness and light weight, makes it become a popular reinforcing material. Our purpose is to estimate its nonlinear mechanical properties by combining Finite Element Method and Molecular Dynamics. According to many researches, the covalent bonds between two nearest-neighboring atoms are simulated as beam elements. The beam properties of the finite element model are obtained from in the modified Morse interatomic potential, and the Young's modulus, Poisson's ratio, Yield strength and Ultimate strength can then be estimated from the plotted stress-strain relation. Although most of the predicted results are in good agreement with the existing data, there is a slight difference in ultimate strength. The difference can be accepted since our simulation is applied to defect-free (without Stone-Wales defect).
The effects of tube type, axial length and element size on the mechanical properties are also discussed. On our investigations, the Young’s modulus ranges from 1 to 1.2 TPa, the Poisson’s ratio from 0.17 to 0.25 and the yield strength from 20 to 30 GPa.

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